Question

a local maximum of the function f(x) occurs for which x - value?

Explanation:

Step1: Recall local - maximum definition

A local maximum of a function is a point where the function value is greater than the values at nearby points.

Step2: Examine the function values in the table

We have the following pairs: $(-4,16),(-3, - 2),(-2,0),(-1,6),(0,0),(1,-2)$.
The function value at $x=-4$ is $16$, at $x = - 3$ is $-2$, at $x=-2$ is $0$, at $x=-1$ is $6$, at $x = 0$ is $0$ and at $x = 1$ is $-2$.
Comparing the values around each $x$-value:

• For $x=-4$, the value of the function at $x=-3$ is $-2$ which is less than $16$.
• For $x=-3$, the value at $x=-2$ is $0$ which is greater than $-2$.
• For $x=-2$, the value at $x=-1$ is $6$ which is greater than $0$.
• For $x=-1$, the value at $x = 0$ is $0$ which is less than $6$.
• For $x=0$, the value at $x = 1$ is $-2$ which is less than $0$.

The largest value among the local - compared values is when $x=-1$ with $f(-1)=6$.

Answer:

$-1$